factoring a trinomial using the x method\nconsider the trinomial $x^{2}+10x + 16$.\nwhich pair of numbers…

factoring a trinomial using the x method\nconsider the trinomial $x^{2}+10x + 16$.\nwhich pair of numbers has a product of $ac$ and a sum of $b$?\nwhat is the factored form of the trinomial?

factoring a trinomial using the x method\nconsider the trinomial $x^{2}+10x + 16$.\nwhich pair of numbers has a product of $ac$ and a sum of $b$?\nwhat is the factored form of the trinomial?

Answer

Explanation:

Step1: Identify a, b, c values

For the trinomial $x^{2}+10x + 16$, we have $a = 1$, $b=10$, $c = 16$. Then $ac=1\times16 = 16$.

Step2: Find two - number pair

We need to find two numbers that multiply to $ac = 16$ and add up to $b = 10$. The numbers are 2 and 8 since $2\times8=16$ and $2 + 8=10$.

Step3: Rewrite the middle - term

Rewrite the trinomial as $x^{2}+2x+8x + 16$.

Step4: Group the terms

Group the terms: $(x^{2}+2x)+(8x + 16)$.

Step5: Factor out the GCF from each group

Factor out the GCF from each group: $x(x + 2)+8(x + 2)$.

Step6: Factor out the common binomial factor

Factor out the common binomial factor $(x + 2)$ to get $(x + 2)(x + 8)$.

Answer:

The pair of numbers is 2 and 8. The factored form of the trinomial is $(x + 2)(x + 8)$.